Alex Levine

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20242026

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5 papers · 1 filter

math.GR2026

Commutative decomposition of infinite symmetric groups and transformation monoids

Luna Elliott, Alex Levine

The commutative subgroup width of a group $G$ is the smallest $k$ such that there are abelian subgroups $A_{0}, A_{1}, \dots, A_{k - 1} \leq G$ with $G = A_{0} A_{1} \dots A_{k - 1}$ . Commutative (i…

math.GR2026

Counting automorphic orbits in finitely generated groups

Luna Elliott, Alex Evetts, Alex Levine

We study an analogue of the conjugacy growth function in finitely generated groups: the automorphic growth function. This counts the number of automorphic orbits that intersect the…

math.GR2025

The Diophantine problem in Thompson's group F

Luna Elliott, Alex Levine

We show that the Diophantine problem in Thompson's group F is undecidable. Our proof uses the facts that F has finite commutator width and rank 2 abelianisation, then uses similar…

math.GR2024

Computing congruences of finite inverse semigroups

Luna Elliott, Alex Levine, James D. Mitchell

In this paper we present a novel algorithm for computing a congruence on an inverse semigroup from a collection of generating pairs. This algorithm uses a myriad of techniques from…

math.GR2024

E-disjunctive inverse semigroups

Luna Elliott, Alex Levine, James Mitchell

In this paper we provide an overview of the class of inverse semigroups $S$ such that every congruence on $S$ relates at least one idempotent to a non-idempotent; such inverse semi…